a.) the three digit number must be even?
Example: TDF-738
1. We choose the last digit (It's the most restrictive)
[where the 8 is in the example from the set {0,2,4,6,8}].
That's 5 ways.
2. We choose the first digit
[where the 7 is in the example from the set {0,1,2,3,4,5,6,7,9)]
That's 9 ways.
3. We choose the middle digit.
(where the 3 is in the example from the set {0,1,2,3,4,5,6,9)]
That's 8 ways.
4. We choose the first letter.
(where the T is in the example from the set
{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
That's 26 ways
5. We choose the second letter.
(where the D is in the example from the set
{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U,V,W,X,Y,Z}
That's 25 ways
5. We choose the last letter.
(where the F is in the example from the set
{A,B,C,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U,V,W,X,Y,Z}
That's 24 ways
Answer 5·9·8·26·25·24 = 5,616,000
------------------------------------------------
b.) the three digit number cannot CONTAIN a 0?
Example: BQK-964
1. We choose the last digit (It's the most restrictive)
[where the 4 is in the example from the set {2,4,6,8}].
That's 4 ways.
2. We choose the first digit
[where the 9 is in the example from the set {1,2,3,5,6,7,9)]
That's 7 ways.
3. We choose the middle digit.
(where the 6 is in the example from the set {1,2,3,5,6,7)]
That's 6 ways.
4. We choose the first letter.
(where the B is in the example from the set
{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
That's 26 ways
5. We choose the second letter.
(where the Q is in the example from the set
{A,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
That's 25 ways
5. We choose the last letter.
(where the K is in the example from the set
{A,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,W,X,Y,Z}
That's 24 ways
Answer 4·7·6·26·25·24 = 2,620,800
Edwin
